Effects of China’s low-carbon policy under stochastic shocks—a multi-agent DSGE model analysis

Abstract

China has announced a target of achieving carbon peaking by 2030 and carbon neutrality by 2060. Therefore, it is important to assess the economic impacts and emission reduction effects of China’s low-carbon policies. In this paper, a multi-agent dynamic stochastic general equilibrium (DSGE) model is established. We analyze the effects of carbon tax and carbon cap-and-trade policies under both deterministic and stochastic conditions, as well as their ability to cope with stochastic shocks. We found that (1) from a deterministic perspective, these two policies have the same effect. Every 1% cut in CO₂ emissions will bring a 0.12% output loss, a 0.5% drop in demand for fossil fuels, and a 0.05% rise in demand for renewable energy; (2) from a stochastic perspective, effects of these two policies are different. This is mainly because economic uncertainty does not change the cost of CO₂ emissions under a carbon tax policy, but it does change the price of CO₂ quotas and the emission reduction behaviors under a carbon cap-and-trade policy; (3) from an economic volatility perspective, both two policies can act as automatic stabilizers. Compared to a carbon tax, a cap-and-trade policy can better ease economic fluctuations. The results of this study provide implications for policy-making.

Introduction

Today, climate change has become a common challenge facing mankind all over the world. Many countries in the world are actively taking action in the international response to climate change. Climate change is moving from a scientific issue to a global political, economic, and social issue (Pinkse and Kolk 2009). As the world’s largest carbon dioxide emitter, the Chinese government attaches great importance to global climate change. China aims to achieve carbon dioxide emission peaking by 2030 and achieve carbon dioxide emission neutrality by 2060. At present, China is at a stage of rapid economic development. In this context, it is important to assess the economic impacts and emission reduction effects of China’s low-carbon/climate policies.

Two types of CO₂ emission reduction methods commonly used internationally are carbon tax and carbon cap-and-trade. Pigou (1920) proposed the concept of an emission tax to internalize external costs of pollutants through taxation. Dales (1968) proposed the concept of emission rights, enabling the emission of pollutants to be traded like a commodity. For a long time, economists have debated fiercely about whether to adopt a carbon tax policy or a carbon cap-and-trade policy (Stavins 2008). After Weitzman (1974), the trade-offs between price-type policies and quantity-type policies have drawn more and more attention. Recently, scholars all over the world have begun to build quantitative policy assessment models to simulate and analyze the economic effects and emission reduction effects of different environmental and climate policies.

Although both carbon tax policy and a carbon cap-and-trade policy affect enterprises’ emission behavior through price leverage, the former is characterized by price control, while the latter is characterized by quantity control. When information is perfectly and there is no uncertainty in the market, the effects of price and quantity policies are the same, and both can achieve Pareto optimality. However, when uncertainty exists, there are significant differences in the performance of price-type and quantity-type policies due to the different mechanisms by which these two policies act on the economy.

With the increasing complexity of national economic structures and the growing international linkages, countries are facing greater uncertainties. These uncertainties are often caused by a series of stochastic shocks that are reflected in all aspects of the economy, such as the impact of oil price fluctuations caused by the volatile international situation on the industrial production and exchange rates of oil-exporting countries (Śmiech et al. 2021), and the impact of the outbreak and global spread of the COVID-19 epidemic on the economic and social activities of developing countries (Mugaloglu et al. 2022). Heutel (2012) and Holladay et al. (2019) pointed out that these shocks not only affect the economy, but also have a non-negligible impact on the effects of climate policies. Therefore, the responsiveness of climate policies to stochastic shocks is also an important indicator for evaluating policy instruments.

Following Nordhaus (1992), which introduced the issue of climate change into economic growth models, the dynamic interactions between the climate and macroeconomics have received wide attention. A large number of researchers have simulated and analyzed various climate policies by constructing “energy-economy-climate” models, for example, system dynamics model (Barisa and Rosa 2018; Xiao et al. 2016), computable general equilibrium (CGE) model (Xiao et al. 2015, 2017; Xu et al. 2018), input–output model (Song et al. 2018), MARKAL (Tsai and Chang 2015), LEAP (Ates 2015) etc. General equilibrium models based on top-down modeling method are more suitable for analyzing the macroeconomic dynamics and the effects of various climate policies. In recent years, CGE models have been widely used to analyze the impacts of various climate policies on macroeconomy. However, the existing CGE models are unable to deal with the deep uncertainties caused by internal or external stochastic shocks. To address this problem, the dynamic stochastic general equilibrium (DSGE) model was developed. DSGE models portray deep uncertainty in the economy by introducing stochastic shocks into the economic system, thus allowing the impact of policies to be analyzed under dynamic and stochastic conditions. In addition, DSGE models also have the advantages of a typical general equilibrium framework, i.e., all markets clear simultaneously, thus allowing for a perfect combination of equilibrium as well as volatility in the economy.

The literatures most closely linked to this paper are researches that have developed in recent years using economic growth models and DSGE models to discuss environmental and climate policy issues (Khan et al. 2019). Acemoglu et al. (2012) introduced endogenous and directed technological change in an economic growth model with limited resources to study dynamic carbon tax policies that maximize welfare. Fischer and Heutel (2013) provided a comprehensive review and summary of research and discussed the DSGE models in environmental and climate economics. In recent years, scholars have gradually started to use DSGE models to study the interactions between economic dynamics and climate policies (Doda 2014; Economides and Xepapadeas 2018; Xiao et al. 2018, 2021; Annicchiarico and Diluiso 2019; Zhao et al. 2020). The milestone studies began with Angelopoulos et al. (2010) and Heutel (2012). Angelopoulos et al. (2010) studied the roles of uncertainty in the welfare ranking of climate policies using a DSGE model. Heutel (2012) studied how climate policy responds to economic fluctuations using a DSGE model that includes an externality.

In recent years, the DSGE model has gradually evolved towards complexity. The multi-sector DSGE model comes from Dissou and Karnizova (2016), who points out the importance of constructing heterogeneous production sectors. They extend the single-sector DSGE model to a multi-sector DSGE model and explore the effects of heterogeneous production sectors on the effects of climate policies. Their study shows that the effects of climate policies are strongly dependent on technology shocks in different sectors, with carbon cap-and-trade policy having the same effect as carbon tax policy when the shocks come from the non-energy sector, and carbon tax policy outperforming carbon cap-and-trade policy when the shocks come from the energy sector. Based on their multi-sector DSGE model, a series of literatures have introduced the energy sectors into the DSGE. Argentiero et al. (2018) develop a DSGE model that includes fossil and renewable energy sources to assess the effectiveness of renewable energy policies. Aminu (2018) develops a DSGE model that includes oil and gas to investigate the impact of oil price shocks and gas price shocks.

The construction and application of multi-sector DSGE models have started relatively late in China. Yang et al. (2016) construct a DSGE model including energy sectors to analyze the macroeconomic effects of energy price shocks. Chao (2017) develops a DSGE model including an oil sector to analyze the effects of exogenous shocks on oil demand. Sun et al. (2021) construct a DSGE model with clean and non-clean energy sources to study the impact of energy technology shocks on sustainable development. Yang et al. (2021) develop a DSGE model with energy production factors to study the impact of energy restructuring on China’s macroeconomy and CO₂ emission reduction. Due to the substitution effects among energy sources, a model that incorporates heterogeneous energy sectors is essential to understand the transmission mechanisms and effects of low-carbon policies. Due to the complex impact mechanisms of climate change, climate quality needs to be characterized and integrated into the production processes of firms and the decision-making processes of residents. Due to the externalities of greenhouse gases, public mitigation actions need to be introduced to avoid the “prisoner’s dilemma” and “tragedy of the commons” caused by climate change. Therefore, the existing DSGE model needs to be further extended in portraying the impact mechanisms of energy substitution, public mitigation behavior, and climate change.

In view of the previous DSGE model, the DSGE model in this paper has been expanded and improved in the following aspects. (1) To characterize the substitution effects among energy sources, we model the energy sector in detail, considering the production processes of fossil and renewable energy sources. (2) To address the externalities of CO₂, we consider the public emission reduction behavior of the government in the emission reduction decision-making, which can reduce the “free-riding” behavior of firms. (3) To address the complex impact mechanism of climate change, we portray the complex relationship between CO₂ emissions, CO₂ concentrations, climate quality, and economic agents. (4) Our model contains multiple agents, which allows us to analyze the optimal interaction of different agents in the economy under different low-carbon policies. (5) We embed different types of stochastic shocks in our DSGE model, which allows us to explore the response of different low-carbon policies to stochastic shocks. Using the model, this paper analyzes the economic impacts and emission reduction effects of carbon tax and carbon cap-and-trade policies in terms of deterministic conditions and stochastic shocks. Furthermore, this paper also analyzes the responses of carbon tax and carbon cap-and-trade policies to a range of stochastic shocks.

The rest of the paper is organized as follows: “Framework of DSGE model” presents the framework of DSGE model. “Effects of low-carbon policies under deterministic conditions” presents the effects of low-carbon policies under deterministic conditions. “Effects of low-carbon policies under stochastic conditions” presents the effects of low-carbon policies under stochastic conditions. “Conclusions and policy implications” presents the conclusions and policy implications.

Framework of DSGE model

Model structure1

1. Firms

The supply side of economy consists of three sectors: one is the final goods sector and the two intermediate goods sectors. The first intermediate goods sector is the renewable energy sector. In a perfectly competitive market, renewable energy firm produces renewable energy $R{E}_t$ by hiring labor $N_t^{\mathit{RE}}$ and leasing capital $K_t^{\mathit{RE}}$:

$$\begin{array}{c}max{\pi }^{\mathit{RE}}=P_t^{\mathit{RE}}R{E}_t-W_t{N}_t^{\mathit{RE}}-R_t^K{K}_t^{\mathit{RE}}\\ s.t.R{E}_t=A_t{(K_t^{\mathit{RE}})}^{{\alpha }_3}{(X_t{N}_t^{\mathit{RE}})}^{1-{\alpha }_3}\end{array}$$ 1

where $P_t^{\mathit{RE}}$ is the price for renewable energy, $W_t$ is nominal wages, $R_t^K$ is nominal prices of capital leases, $A_t$ is total factor productivity, and ${\chi }_t$ is the negative effect of climate change on labor supply.

The second intermediate goods sector is the fossil fuel sector, which represents a fossil fuel mining firm that employs capital $N_t^{\mathit{EN}}$ and labor $K_t^{\mathit{EN}}$ to extract fossil fuel $E{N}_t$. Government imposes fossil fuel tax at tax rate ${\tau }_t^{\mathit{EN}}$ to limit over-exploitation of fossil resources:

$$\begin{array}{c}max{\pi }^{\mathit{EN}}=(1-{\tau }_t^{\mathit{EN}})P_t^{\mathit{EN}}E{N}_t-W_t{N}_t^{\mathit{EN}}-R_t^K{K}_t^{\mathit{EN}}\\ s.t.E{N}_t=A_t{(K_t^{\mathit{EN}})}^{{\alpha }_2}{({\chi }_t{N}_t^{\mathit{EN}})}^{1-{\alpha }_2}\end{array}$$ 2

The final goods firms produce final output $Y_t$ by hiring labor $N_t^Y$, leasing capital $K_t^Y$, and purchasing fossil fuel and renewable energy:

$$Y_t=A_t{({\chi }_t{N}_t^Y)}^{{\mathrm{\Delta }}_1}{(K_t^Y)}^{{\alpha }_1}{(q_{t}E{N}_t)}^{{\varphi }_1}{(R{E}_t)}^{(1-{\alpha }_1-{\mathrm{\Delta }}_1-{\varphi }_1)}$$ 3

where $q_t$ is the efficiency of fossil fuel input. Following the “learning by doing” process, we believe that improved energy efficiency can be attributed to energy use, which means $q_t=f_t^{\mathit{EN}}E{N}_t^{(\gamma -1)}$ holds.

The production behavior involves the use of fossil fuel, which can lead to CO₂ emissions. Meanwhile, final goods firms have private emission reduction behaviors, which are expressed by $D_t$. The stock of CO₂ is similar to the stock of capital, depreciated at a rate of ${\delta }_S$. $Q_t$ represents the public emission reduction behaviors caused by government public governance actions. $\phi$ is the coefficient of public fiscal emission reduction inputs. This setting can reduce the “free-riding” behavior of firms due to the public goods attribute of climate governance. Thus, CO₂ emissions $M_t$ and the stock of CO₂ emissions $S_t$ are shown in Eqs. (4) and (5):

$$M_t=\varpi (1-D_t)E{N}_t$$ 4

$$S_{t+1}=S_t-{\delta }_S{S}_t+M_t-\phi Q_t$$ 5

Final goods firms’ emission reduction behaviors can bring emission reduction costs. With reference to Annicchiarico and Di Dio (2015), the total emission reduction costs $E{R}_t$ are shown in Eq. (6):

$$E{R}_t={\psi }_1{D}_t^{{\psi }_2}{Y}_t$$ 6

Climate change can bring negative effects to the residents, thus affecting labor efficiency. We use a production function that includes the effects of CO₂ stock:

$${\chi }_t=1-{\omega }_0-{\omega }_1{S}_t^2-{\omega }_2{S}_t$$ 7

Thus, a representative final goods firm maximizes the profits under the constraint of production capacity:

$$\begin{array}{c}max{\pi }^Y=P_t{Y}_t-W_t{N}_t^Y-R_t^K{K}_t^Y-P_t^{CO2}{M}_t-P_t^{\mathit{EN}}E{N}_t-P_t^{\mathit{RE}}R{E}_t-E{R}_t\hfill \\ s.t.Y_t=A_t{(X_t{N}_t^Y)}^{{▵}_1}{(K_t^Y)}^{{\alpha }_1}{(R{E}_t)}^{{\varphi }_1}{\left[q_t,E,N_t\right]}^{(1-{\alpha }_1-{▵}_1-{\varphi }_1)}\hfill \end{array}$$ 8

• 2.Resident

The economy contains countless homogeneous residents, each of which own labor and capital and enters a fully competitive factor market. Firms produce by leasing homogenized labor and capital from residents. We assume that any resident has the same preferences, has the same utility function, and can survive indefinitely. The utility function for a representative resident takes the form of constant relative risk aversion:

$$\underset{(C_t,N_t,K_t,B_t,I_t)}{U_t}=E_t\sum _{t=0}^{\infty }{\beta }^t{s}_t^c{\chi }_t(\ln C_t-\frac{N_t^{1+\theta }}{1+\theta })$$ 9

where $U_t$ is the utility, $E_t$ is the conditional expectation based on period t, $C_t$ is consumption, and $N_t$ is total labor supply.

A representative resident maximizes its utility by planning its consumption, labor supply, investment, and bonds acquisition. In period t, a representative resident needs to meet the following budget constraint:

$$P_t{C}_t+P_t{I}_t+B_t-R_{t-1}^B{B}_{t-1}-(1-{\tau }_t^N)W_t{N}_t-(1-{\tau }_t^K)R_t^K{K}_{t-1}\le 0$$ 10

where $P_t$ is the overall price level, $I_t$ is investment, $B_t$is bond issued by the government, and $R_t^B$ is government bond price.

The capital accumulation equation is Eq. (11). ${\delta }_K$ is the depreciation rate of capital. In addition, in the process of capital formation, investment adjustment incurs certain costs:

$$K_t-(1-{\delta }_K)K_{t-1}=s_t^I[1-{(\frac{I_t}{I_{t-1}}-1)}^2]I_t$$ 11

A representative resident maximizes its utility under budget constraints. ${\lambda }_t$ and ${\xi }_t$ are the Lagrangian multipliers of the budget constraint and capital accumulation equation respectively. F.O.Cs for Lagrangian function are as follows:

$${\chi }_t{s}_t^c={\lambda }_t{P}_t{C}_t$$ 12

$${\chi }_t{s}_t^c{N}_t^{\theta }={\lambda }_t(1-{\tau }_t^N)W_t$$ 13

$${\xi }_t+\beta E_t[{\lambda }_{t+1}(1-{\tau }_{t+1}^K)R_{t+1}^K-(1-{\delta }_K){\xi }_{t+1}]=0$$ 14

$${\lambda }_t=\beta E_t[(1+R_{t+1}^B){\lambda }_{t+1}]$$ 15

$${\lambda }_t{P}_t=-{\xi }_t{s}_t^I[1-{(\frac{I_t}{I_{t-1}}-1)}^2]+2{\xi }_t{s}_t^I{I}_t(\frac{I_t}{I_{t-1}^2}-\frac{1}{I_{t-1}})-2\beta E_t[{\xi }_{t+1}{s}_{t+1}^I\frac{I_{t+1}^2}{I_t^2}(\frac{I_{t+1}}{I_t}-1)]$$ 16

• 3.Government

For the externalities caused by CO₂ emissions, the government has three choices. It can choose to do nothing or levy tax on CO₂ emission or set an emission cap and auction all the CO₂ quotas. Thus, government obtains the revenue through CO₂ revenues, taxes, and bonds. At the same time, revenues from CO₂ emissions are all used to reduce CO₂ emissions publicly, which means $Q_t=P_t^{CO2}{M}_t$ holds. The government’s budget constraint is

$$P_t{G}_t+R_{t-1}^B{B}_{t-1}+Q_t=B_t+{\tau }_t^N{W}_t{N}_t+{\tau }_t^K{R}_t^K{K}_t+{\tau }_t^{\mathit{EN}}{P}_t^{\mathit{EN}}E{N}_t+P_t^{CO2}{M}_t$$ 17

• 4.Market clearing and stochastic shocks

Labor and capital markets clearing hold:

$$K_t=K_t^Y+K_t^{\mathit{EN}}+K_t^{\mathit{RE}}$$ 18

$$N_t=N_t^Y+N_t^{\mathit{EN}}+N_t^{\mathit{RE}}$$ 19

The model in this paper contains seven stochastic shocks, namely, subjective discount rate shock (${\epsilon }_{t,s^c}$), investment adjustment cost shock (${\epsilon }_{t,s^I}$), public expenditure shock (${\epsilon }_{t,G}$), labor tax rate shock (${\epsilon }_{t,{\tau }^N}$), capital tax rate shock (${\epsilon }_{t,{\tau }^K}$), and energy efficiency shock (${\epsilon }_{t,f^{\mathit{EN}}}$).

$$ln{X}_t={\rho }_{X}ln{X}_{t-1}+{\epsilon }_{t,X}{\epsilon }_{t,X}\sim i.i.d.N(0,{\sigma }^2)$$ 20

where $X_t=\{s_t^c,s_t^I,G_t,{\tau }_t^K,{\tau }_t^N,f_t^{\mathit{EN}}\}$, ${\epsilon }_{t,X}=\{{\epsilon }_{t,s^c},{\epsilon }_{t,s^I},{\epsilon }_{t,G},{\epsilon }_{t,{\tau }^K},{\epsilon }_{t,{\tau }^N},{\epsilon }_{t,f^{\mathit{EN}}}\}$ are the stochastic shocks, which are normally distributed; ${\rho }_X=\{{\rho }_{s^c},{\rho }_{s^I},{\rho }_G,{\rho }_{{\tau }^K},{\rho }_{{\tau }^L},{\rho }_{f^{\mathit{EN}}}\}$are autoregressive coefficients.

Model calibration and estimation

1. Model calibration

According to the economic situation and previous literatures, we calibrated some structural parameters of the model. The parameter calibration results can be found in Table 1.

Table 1.

The calibration results

	Value	Description	Source
β	0.95	Discount rate	Ríos-Rull et al. (2009); Fischer and Springborn (2011)
θ	1.97	Inverse of the Frisch elasticity of labor supply	Lintunen and Vilmi (2013); Pop (2017)
${\alpha }_1$	0.33	Capital-output elasticity	Leeper and Yang (2008); Fischer and Springborn (2011); Nalban (2018)
${\mathrm{\Delta }}_1$	0.58	Labor-output elasticity	Leeper and Yang (2008); Fischer and Springborn (2011); Nalban (2018)
${\varphi }_1$	0.08	Fossil fuel-output elasticity	Estimated based on input–output data of China
${\alpha }_2$	0.593	Capital-fossil fuel elasticity	Estimated based on input–output data of China
${\alpha }_3$	0.558	Capital-renewable energy elasticity	Estimated based on input–output data of China
γ	2.136	Energy efficiency elasticity	Shao et al. (2013)
$\varpi$	0.6	CO2 emission coefficient	Field et al. (2014)
${\omega }_0$	1.395E − 03	Labor efficiency loss parameter	Annicchiarico and Di Dio (2015); Wu (2017)
${\omega }_1$	− 6.67E − 06
${\omega }_2$	1.5E − 08
$\phi$	0.5	Coefficient of public emission reduction inputs	Angelopoulos et al. (2010)
${\psi }_1$	0.185	Emission reduction cost coefficient	Xu et al. (2016)
${\psi }_2$	2.8	Emission reduction cost parameter	Xu et al. (2016)
${\delta }_S$	0.005	CO2 degradation rate	Nordhaus (1991); Falk and Mendelsohn (1993)
${\delta }_K$	0.025	Capital depreciation rate	Chang and Kim (2007)

For the resident, the parameters that need to be calibrated are β, θ, ${\delta }_K$. For the discount rate β, many scholars set its value around 0.95 (Ríos-Rull et al. 2009; Fischer and Springborn 2011). The quarterly capital depreciation rate ${\delta }_K$ is set at 2.5% by many scholars (Chang and Kim 2007). The inverse of the Frisch elasticity of labor supply θ is calibrated Referring to Lintunen and Vilmi (2013) and Pop (2017).

The output elasticities of factors that need to be calibrated in the production functions are ${\alpha }_1$, ${\alpha }_2$, ${\alpha }_3$, ${\mathrm{\Delta }}_1$, ${\varphi }_1$, γ. Most scholars estimated that the capital-output elasticity ${\alpha }_1$ is about 0.35, and the labor-output elasticity ${\mathrm{\Delta }}_1$ is about 0.6 (Leeper and Yang 2008; Fischer and Springborn 2011; Nalban 2018). The capital-fossil fuel elasticity ${\alpha }_2$ capital-renewable energy elasticity ${\alpha }_3$ fossil fuel-output elasticity ${\varphi }_1$ are estimated from input–output data of China. We set China’s energy efficiency elasticity $\gamma$ as in Shao et al. (2013).

Turning to the calibration regarding CO₂ emissions, we set labor efficiency loss parameters ${\omega }_0$, ${\omega }_1$_, and ${\omega }_2$ as in Annicchiarico and Di Dio (2015) and Wu (2017). The effect coefficient of public fiscal emission reduction inputs, $\phi$, is set at 0.5, referring to Angelopoulos et al. (2010). For emission reduction cost parameters ${\psi }_1$ and ${\psi }_2$, we refer to Xu et al. (2016). The CO₂ emission coefficient $\varpi$ is calculated from the IPCC greenhouse gas emissions inventory and the third assessment report (Field et al. 2014). The natural degradation rate parameters for CO₂ ${\delta }_S$ is calibrated from Nordhaus (1991) and Falk and Mendelsohn (1993).

• 2.Model estimation

For dynamic depth structure parameters in the model, we chose the method of Bayesian estimation to extract them from economic behavior. According to the availability of data, China’s GDP, resident consumption, fossil fuel consumption, and investment quarterly data from 2001 Q1 to 2017 Q4 (68 quarters) were selected as Bayesian estimation observation data. Since the data are measured quarterly, we used Census X12 to strip out the seasonality of the data. For the growth trend of data, we used one-side-HP-filter to eliminate the growth trend of economic data and separate the fluctuation of data. In the process of Bayesian estimation, we used Markova Chain Monte Carlo method to randomly sample 30,000 times. The prior means of the first-order autoregressive coefficients of exogenous shocks are all set at 0.8, and the prior distribution are all set as beta distribution. The prior distribution and posterior distribution of depth structure parameters are shown in Table 2.

Table 2.

The Bayesian estimation results

	Prior distribution			Post distribution
	Shape	Mean	Std. dev	90% confidence interval		Mean
${\rho }_{s^c}$	beta	0.8	0.1	0.8056	0.646	0.9667
${\rho }_{s^I}$	beta	0.8	0.1	0.7874	0.6364	0.9528
${\rho }_{f^{\mathit{EN}}}$	beta	0.8	0.1	0.7014	0.4991	0.9037
${\rho }_G$	beta	0.8	0.1	0.6973	0.6956	0.699
${\rho }_{{\tau }^K}$	beta	0.8	0.1	0.7987	0.6547	0.9718
${\rho }_{{\tau }^N}$	beta	0.8	0.1	0.788	0.6406	0.9329

The estimation results show that the capital tax rate shock is the most persistent, while the public expenditure shock is the least persistent of all shocks. Since the accumulation of capital is a slow process, this leads to a long-lasting impact of capital tax rate shock and investment adjustment cost shock on the economy. Public expenditure has a more rapid impact on the economy, which leads to the fact that public spending shock does not last for a long time. As important factor inputs, labor tax rate shock that affect labor inputs also has long-term effects on the economy.

Settings of low-carbon policy

In what follows, we will consider three different low-carbon policy regimes:

Baseline scenario

Firms do not bear the cost of CO₂ emissions. The government neither levies a carbon tax nor establishes a carbon cap-and-trade market. Therefore, the price of CO₂ emissions is zero.

Carbon tax policy scenario

The government internalizes the external costs of CO₂ emissions by imposing a carbon tax on firms that emit CO₂. The price per unit of CO₂ is therefore equal to the tax rate.

Carbon cap-and-trade policy scenario

The government establishes a carbon market to reduce CO₂ emissions. The government sets a cap on total CO₂ emissions and sells CO₂ emission quotas to firms that emit CO₂. The price of CO₂ emissions quotas is determined by market.

Before we proceed, a remark is in order. To make the results of carbon tax and carbon cap-and-trade comparable, we set the same emission reduction ratio. Under both carbon tax and carbon cap-and-trade policies, the emission reduction ratios are all 40% compared with baseline scenario.

Effects of low-carbon policies under deterministic conditions

In this section, we simulated the effects of carbon tax and carbon cap-and-trade policies under deterministic conditions. The results in Table 3 show the mean and standard deviation of main variables in carbon tax policy scenario and carbon cap-and-trade policy scenario.

Table 3.

Effects of carbon tax and carbon cap-and-trade policies

	Baseline case		Carbon tax case			Carbon cap-and-trade case
	Mean	Std. dev	Mean	Change	Std. dev	Mean	Change	Std. dev
Utility	−7.964	1.655	−8.897	−11.72%	1.666	−8.897	−11.72%	1.518
Output	1.079	0.083	1.031	−4.46%	0.079	1.031	−4.46%	0.072
Consumption	0.869	0.071	0.826	−4.91%	0.068	0.826	−4.91%	0.061
Investment	0.110	0.017	0.101	−8.40%	0.015	0.101	−8.40%	0.013
Labor	0.915	0.004	0.910	−0.48%	0.004	0.910	−0.48%	0.004
Wage	0.767	0.060	0.723	−5.80%	0.057	0.723	−5.80%	0.050
Fossil fuel	0.376	0.031	0.300	−20.23%	0.024	0.300	−20.23%	0.012
Renewable energy	0.021	0.002	0.021	1.93%	0.002	0.021	1.93%	0.002
Renewable energy price	0.492	0.004	0.505	2.64%	0.004	0.505	2.64%	0.005
Emission reduction	0.000	0.000	0.248	0.00%	0.001	0.248	0.00%	0.030
CO2 emissions	0.226	0.018	0.135	−40.00%	0.011	0.135	−40.00%	0.000

In the case of achieving the same reduction ratio, the effects of both policies are the same under deterministic conditions. Compared with the baseline scenario, the implementation of low-carbon policies has a negative impact on economic growth. From the perspective of total output, the implementation of low-carbon policies reduces total output by 4.46%; meanwhile, consumption decreases by 4.91%, and investment decreases by 8.4%. Residents’ utility decreases by 11.72% due to reduced consumption and wages. There is no doubt that low-carbon policies can curb long-term economic growth. As carbon prices rise, firms must pay extra costs. Therefore, there are trade-offs between reducing emissions and paying the price of carbon emissions. In the baseline scenario, because the carbon price is zero and the final goods firms have no incentive to reduce CO₂ emissions, there is no private emission reduction effort. When the carbon cost rises, firms have incentives to reduce CO₂ emissions, so the private emission reduction efforts increase to 24.8%, that is, carbon emission intensity of fossil fuel is reduced from 0.6 to 0.4512. The decline in the demand for labor by firms resulted in a 0.48% decrease in the labor supply of residents and a 5.8% decrease in wages. At the same time, labor efficiency has increased slightly due to the decline in CO₂ emissions. Since the use of fossil fuel will directly lead to CO₂ emissions, the cost of using fossil fuel will increase after the implementation of low-carbon policies. As a result, the final goods firms’ demand for fossil fuel drops by 20.23%. At the same time, the final goods firms tend to use clean renewable energy. As a result, the consumption of renewable energy increases by 1.93%, which causes the price of renewable energy to rise by 2.64%.

The standard deviations of the variables in different scenarios reflect the fluctuations of the variables near their means. Scenarios with a small standard deviation indicate that economic fluctuations are relatively gentle, and vice versa. The standard deviations of variables in the carbon cap-and-trade policy scenario are all smaller than in the carbon tax policy scenario.

Effects of low-carbon policies under stochastic conditions

The above analysis focused on the macroeconomic effects of two different low-carbon policies, without considering the potential impact of various stochastic shocks on the effects of these two policies. In this section, we will introduce stochastic shocks in the resident sector, government sector, and production sector into the DSGE model, with the aim of analyzing the effects of the two low-carbon policies under various stochastic shocks.

Unexpected shocks in firm sector

Figure 1 shows the dynamic responses to an energy efficiency shock with a standard deviation of 1%. Due to the improvement of energy efficiency, the marginal output of energy increases, so the optimal decision for firms is to reduce energy input. However, as a result of the decline in real energy prices caused by the improvement in energy efficiency, the income effects of firms lead to the increase in their demand for energy. The energy efficiency rebound occurs when higher demand for energy offsets a reduction in energy consumption due to improvements in energy efficiency. Whether energy efficiency rebound will occur is a widely debated issue. Our simulation results show that as energy efficiency increases, energy demand increases. In fact, this proves that the energy efficiency rebound effect does occur. The marginal technological replacement rate of energy is rising as firms become more energy efficient. Therefore, firms will employ more labor and lease more capital to carry out production activities. As a result of the increase of input factors, the total output of the society rises, showing pro-periodicity. As the economy temporarily booms, CO₂ emissions rise.

Fig. 1.

The dynamic responses of variables to an energy efficiency shock

The response of the macroeconomic variables to an energy efficiency shock differs in the carbon tax and carbon cap-and-trade scenarios. As the results obtained in the above section, both the carbon tax and carbon cap-and-trade policies raise the production costs of firms. Some of the resources in the economy are allocated to emission reduction, thus negatively affecting the economic growth. Thus, the implementation of low-carbon policies weakens the expansionary effect.

The response of key economic and climate variables to energy efficiency shocks in the carbon tax scenario is similar to that in the baseline scenario. In the carbon tax scenario, the marginal cost of per unit intermediate goods comprises the marginal cost of the good and the marginal abatement cost of CO₂. In the face of an energy efficiency shock, a rational firm will always choose to make its marginal abatement cost equal to the tax rate on per unit of CO₂ emissions. Since firms face a fixed price for CO₂ emissions, their marginal abatement costs also remain constant. Thus, the carbon tax exerts less emission reduction pressure than a cap-and-trade policy.

When government implements a carbon cap-and-trade policy, firms must invest more resources to reduce CO₂ emissions as they expand their output. Unlike carbon tax policy, the price of CO₂ quotas is affected by total energy efficiency shocks under a carbon cap-and-trade policy. A rational firm will still choose to make its marginal abatement cost equal to the per unit of CO₂ quota price. When the economy faces an energy efficiency shock, firms are under stronger pressure to reduce emissions and thus have greater demand for CO₂ quotas. The price of CO₂ quotas rises as the demand for CO₂ quotas rises, which also leads to a larger increase in the abatement costs. As a result, both the proportion of emission reductions and the total abatement cost rise in the carbon cap-and-trade policy scenario.

Unexpected shocks in resident sector

The unexpected shocks in resident sector include two kinds of exogenous shocks, that is, the subjective discount rate shock and the investment adjustment cost shock. Subjective discount rate shock mainly affects residents’ utilities and investment adjustment cost shock mainly affects residents’ investment decisions. The dynamic responses of macroeconomic variables in resident sector under carbon tax and cap-and-trade policies are shown in Fig. 2.

Fig. 2.

The dynamic responses of variables to unexpected shocks in resident sector

Figure 2a shows the dynamic responses to a subjective discount rate shock with a standard deviation of 1%. When residents’ expectations for the discount rate increase, macroeconomic variables such as capital, labor, and output are all negatively impacted. A higher discount rate means that the potential costs of future consumption by residents rise. Therefore, residents tend to consume in the current period. When consumption positively deviates from its steady state value, the proportion of residents’ disposable income used for investment will decrease, which will have a negative impact on social capital accumulation. Higher discount rates also have an impact on residents’ intertemporal optimization behavior. For example, residents prefer the current leisure time, which reduces the labor supply. The negative effects of factors such as capital, investment, and labor will lead to less hired labor and less used other factors for production, which will result in a decline in total social output. Due to the temporary recession in the economy, the demand for fossil fuel and renewable energy decrease, so CO₂ emissions and their stocks also decrease.

We now look at the differences in the economic dynamics under carbon tax and cap-and-trade policies. The consumption, capital, and labor are most sensitive in the baseline scenario and least sensitive in the cap-and-trade policy scenario. The responses of fossil fuel inputs and CO₂ emissions to a subjective discount rate shock vary greatly in different scenarios. Compared to baseline scenario, the decline in CO₂ emissions is smaller under the carbon tax. The additional costs associated with fossil-fuel emissions lead to a decline in fossil fuel inputs. For the cap-and-trade policy, because the government sets the upper limit of emissions, firms cannot change their CO₂ emissions. They can only meet the emission cap by controlling their own private emission reduction efforts and reducing fossil fuel inputs. The economic downturn leads to insufficient demand for quotas, carbon prices fall sharply, and firms’ willingness to reduce emissions also falls sharply. Although demand for fossil fuel decline, the decline under cap-and-trade policy is the smallest in all scenarios. This is because the greatly reduced carbon price can greatly reduce the use cost of fossil fuel, making fossil fuel less expensive than renewable energy. As a result, firms’ demand for renewable energy will be decreased.

Figure 2b shows the dynamic responses to an investment adjustment cost shock with a standard deviation of 1%. Note that this shock means a lower investment adjustment cost. Thus, under this shock, capital adjusts positively. Due to the increase of investment and capital stock, the economy experiences a small-scale expansion effect, and the demand for labor of firms increases. As demand for factors of production rises, firms’ outputs adjust positively, resulting in an increase in total social output. At the same time, CO₂ emissions rise with economic expansion.

Since firms do not need to bear the external costs of CO₂ emissions, the economic expansion is the largest in the baseline scenario. In the cap-and-trade policy scenario, in order to achieve the same CO₂ emissions, firms can choose to reduce their fossil fuel input while paying less emission reduction efforts, or increase their fossil fuel input while increasing their emission reduction efforts. Obviously, firms choose the latter. As a result of the economic expansion, firms’ demand for labor and capital will increase, leading to a rise in the marginal output of fossil fuel. Therefore, they still tend to use more fossil fuel. Because CO₂ emissions are strictly limited, the emission costs borne by firms are the largest, and therefore, the degree of economic expansion is the smallest. Faced with the highest pressure to reduce emissions, firms are more inclined to use renewable energy. Therefore, the increase in demand for fossil fuel under a cap-and-trade policy is less than that in baseline scenario and under a carbon tax policy, while the increase in demand for renewable energy is greater than that in baseline scenario and under a carbon tax policy. It is worth noting that although firms are reducing CO₂ emissions by increasing renewable energy input, the demand for renewable energy is rising only slightly because of the high cost of using renewable energy.

Unexpected shocks in government sector

The unexpected shocks in government sector include three kinds of exogenous shocks: labor tax rate shock, capital tax rate shock, and public expenditure shock. The dynamic responses of macroeconomic variables in government sector under the carbon tax and cap-and-trade policies are shown in Fig. 3.

Fig. 3.

The dynamic responses of variables to unexpected shocks in government sector

Figure 3 a shows the dynamic responses to a capital tax rate shock with a standard deviation of 1%. An increase in the capital tax rate means a reduction in the return on capital, which will cause residents to save less and invest less. As a result, the capital stock will be negatively impacted. Insufficient social investment leads to the inability of firms to expand production, thus reducing the demand for residents’ labor. The decrease of the demand for various factors of production eventually leads to the decrease of the total output of the society.

The response of key macroeconomic variables to capital tax rate shocks varies considerably in the scenarios of carbon tax and carbon cap-and-trade policies. Compared to the baseline scenario, the low-carbon policies compensate for the negative impacts of capital tax rate shocks on the economy. The simulation results show that the economy suffers the least negative effects under the cap-and-trade policy, followed by the carbon tax scenario and then the baseline scenario. When the economy suffers a negative shock, a fall in the level of the economy leads to a reduction in the output of firms and a consequent fall in their demand for various production factors. The fall in energy demand also tends to reduce CO₂ emissions, which leads to a fall in the price of CO₂ quotas. As a result, firms invest fewer resources to reduce CO₂ emissions. This reduction in emission reduction costs allows firms to have more resources available for their production and therefore more scope for production decisions to counteract the fall in output. Therefore, the above reasons allow the carbon cap-and-trade policy to mitigate the economic contraction effect caused by the capital tax rate shocks.

Figure 3b shows the dynamic responses to a labor tax rate shock with a standard deviation of 1%. As a result of the increase in the labor tax rate, the income of residents falls, and so does the opportunity cost of leisure. Therefore, residents prefer leisure and choose to supply less labor. At the same time, the economy as a whole will experience a small recession as lower disposable incomes depress resident investment and consumption. The decline in fossil fuel inputs is accompanied by the decrease of firms’ private emission reduction efforts and emission reduction costs. Similar to capital tax rate shocks, both carbon tax and cap-and-trade policies slightly alleviate the negative impacts of labor tax rate shock on macroeconomy. Notably, capital stock and labor supply are least negatively affected under the cap-and-trade policy scenario. Thus, this policy enhances the ability of capital and labor markets to respond to stochastic shocks.

Figure 3c shows the dynamic responses to a government public expenditure shock with a standard deviation of 1%. In terms of various macroeconomic variables, labor, fossil fuel and renewable energy, and output all increase. The government’s expansionary fiscal policy will drive economic growth, but at the same time, there will be a crowding out effect, and private consumption and investment will be negatively impacted. As fossil fuel inputs increase in all three scenarios, CO₂ emissions increase accordingly. The baseline scenario saw the largest increase in energy input. CO₂ emissions in the baseline scenario are higher than that in carbon tax and cap-and-trade policy scenarios.

Economic fluctuations

The effects of economic fluctuations caused by stochastic shocks can vary considerably under different low-carbon policies. Thus, economic volatility is another important criterion for evaluating the merits of different low-carbon policies. The fluctuations of consumption, fossil fuel, investment, labor, output, and CO₂ emissions in three scenarios are shown in Fig. 4.

Fig. 4.

The economic fluctuations in three scenarios

The results show that consumption and investment fluctuate in line with output and are pro-cyclical. The volatility of CO₂ emissions in both the carbon tax and the carbon cap-and-trade scenarios is smaller than in the baseline scenario. Therefore, both low-carbon policies can mitigate the volatility of CO₂ emissions with economic fluctuations.

In the baseline scenario, consumption, fossil energy, investment, labor, and output fluctuate the most. When the government implements any of the low-carbon policies, the volatility of the economy decreases. Thus, both low-carbon policies act as automatic stabilizers in smoothing economic macroeconomic fluctuations. The simulation results also show that the carbon cap-and-trade policy has a stronger stabilizing effect on the economy than the carbon tax policy. Carbon cap-and-trade policy largely mitigates the volatility of CO₂ emissions, which in turn mitigates the volatility of energy markets in response to stochastic shocks. As a result, an economy implementing a carbon cap-and-trade policy is less volatile and more resilient to stochastic shocks.

Sensitivity analysis

Sensitivity analysis is used to evaluate the sensitivity of model outputs to inputs. We can identify the sensitivity of the model to each parameter or variable through sensitivity analysis and conduct model uncertainty analysis on this basis. Therefore, this paper analyzes the sensitivity of the steady-states as well as impulse responses of the model to some key parameters under single-factor changes.

1. Steady-states

We analyze the sensitivity of the steady-states of the main variables to three parameters, elasticity of labor supply, CO₂ emission coefficient, and emission reduction cost coefficient. Table 4 shows the results of the sensitivity analysis of steady-states.

Table 4.

The sensitivity analysis results of steady-states to parameters

	Carbon tax case
		Elasticity of labor supply		CO2 emission coefficient		Emission reduction cost coefficient
	Mean	Mean	Change (−1%)	Mean	Change (+ 1%)	Mean	Change (+ 1%)
Consumption	0.826	0.782	−0.11%	0.815	−0.04%	0.824	−0.01%
Fossil fuel	0.3	0.286	−0.09%	0.284	−0.16%	0.295	−0.03%
Capital	4.037	3.842	−0.10%	3.955	−0.06%	4.01	−0.01%
Labor	0.91	0.873	−0.08%	0.91	0.00%	0.91	0.00%
Renewable energy	0.021	0.02	−0.10%	0.021	−0.01%	0.021	−0.01%
CO2 stocks	23.835	22.73	−0.09%	28.637	0.60%	25.292	0.10%
Final output	1.031	0.981	−0.10%	1.02	−0.03%	1.027	−0.01%
CO2 emissions	0.136	0.129	−0.09%	0.163	0.60%	0.144	0.10%
Emission reduction	0.248	0.248	0.00%	0.284	0.43%	0.188	−0.39%

When the elasticity of labor supply decreases, variables such as output, consumption, capital, fossil energy output, and renewable energy output decrease. For every 1% decrease in elasticity of labor supply, output decreases by 0.1% on average. When the CO₂ emission coefficient increases, it means that the intensity of CO₂ emission increases. For every 1% increase in CO₂ emission coefficient, output decreases by 0.03% on average. When the emission reduction cost coefficient increases, it means that the cost of emission reduction increases. For every 1% increase in emission reduction cost coefficient, output decreases by 0.006% on average.

• 2.Impulse responses

We analyze the sensitivity of impulse responses of output to the three parameters, elasticity of labor supply, CO₂ emission coefficient, and emission reduction cost coefficient. Figure 5 shows the results of the sensitivity analysis of impulse responses.

Fig. 5.

The sensitivity analysis results of impulse responses to parameters

The trend of impulse responses of output response to stochastic shocks is essentially the same for different parameter values. The impulse responses of output response to stochastic shocks when CO₂ emission coefficient and emission reduction cost coefficient are changed are essentially the same as the impulse responses of output response to stochastic shocks in the carbon tax scenario. As we obtained above, the sensitivity of the model steady-state results to the elasticity of labor supply is the largest of the three parameters. So, the changes in labor supply elasticity cause the largest changes in the impulse responses of output response to stochastic shocks.

Conclusions and policy implications

In this paper, we established a multi-agent DSGE model that considers energy substitution effects, public emission reduction decisions, and the impact mechanisms of climate quality. With this model, we not only analyzed the economic impacts and emission reduction effects of carbon tax and carbon cap-and-trade policies under both deterministic conditions and stochastic shocks, but also their ability to respond to stochastic shocks. The results are as follows:

From a deterministic perspective, both the carbon tax and carbon cap-and-trade policies have the same effect when the same percentage of CO₂ reductions is achieved. The implementation of the low-carbon policies will have a negative impact on economic growth. Every 1% cut in CO₂ emissions will bring 0.12% output cost and 0.3% welfare reduction. At the same time, the carbon tax and cap-and-trade will promote emission reduction and improve the energy structure. Every 1% CO₂ emission reduction will increase the level of reduction efforts by 0.62%, reduce the demand for fossil energy by 0.5%, and increase the demand for renewable energy by 0.05%.

After introducing a range of stochastic shocks, there are differences in the effects of these two policies. The difference between the economic dynamics in the carbon tax scenario and the baseline scenario is relatively small. In the carbon tax scenario, firms face a fixed price on CO₂ emissions, and their share of emission reductions is always maintained at a level where the marginal abatement cost equals the carbon tax rate. Unlike the carbon tax policy, firms’ abatement behavior under carbon cap-and-trade policy is influenced by market price of CO₂ quotas. When the economy is hit by a negative shock, the reduction in abatement costs under a carbon cap-and-trade policy allows firms to have more resources available for their production and therefore more scope for production decisions to counteract the fall in output. Thus, a carbon cap-and-trade policy can mitigate the negative effects to a greater extent than a carbon tax.

From an economic volatility perspective, economic fluctuation is lowest under a carbon cap-and-trade policy, followed by a carbon tax policy, and highest under the baseline scenario. Both the carbon tax and carbon cap-and-trade policies can act as automatic stabilizers. Compared with the carbon tax policy, the carbon cap-and-trade policy has a stronger stabilizing effect on the economy. An economy with a carbon cap-and-trade policy in place can better cope with stochastic shocks.

Some implications for policy-making can be gained from the results, which will help the government to choose a low-carbon policy more suitable for the economic development. When the economy does not face any uncertainty, both carbon tax and carbon cap-and-trade policies can be chosen as the CO₂ emission reduction policy, because both have the same effect in a perfect market situation. However, the macroeconomy always operates under various uncertainties and stochastic shocks. Therefore, the government needs to take into account the impact of uncertainties on policy effects when making policy choices. Compared with the carbon tax policy, carbon cap-and-trade policy can better cope with the stochastic shocks and has a better automatic stabilizer effect. When the economy faces uncertainties, carbon cap-and-trade policy should be chosen as the CO₂ emission reduction policy.

Appendix

Table 5

Table 5.

Variable list

	Description		Description		Description
${\mathit{RE}}_t$	Renewable energy	$W_t$	Wages	${\tau }_t^{\mathit{EN}}$	Fossil fuel tax rate
$P_t^{\mathit{RE}}$	Renewable energy price	$R_t^K$	Capital leases price	${\mathit{EN}}_t$	Fossil fuel
$N_t^{\mathit{RE}}$	Labor inputs (renewable energy)	$A_t$	Total factor productivity	$P_t^{\mathit{EN}}$	Fossil fuel price
$K_t^{\mathit{RE}}$	Capital inputs (renewable energy)	${\chi }_t$	Labor efficiency	$N_t^{\mathit{EN}}$	Labor inputs (fossil fuel)
$U_t$	Utility	$Q_t$	Public emission reduction	$K_t^{\mathit{EN}}$	Capital inputs (fossil fuel)
$C_t$	Consumption	$N_t$	Total labor supply	${\mathit{ER}}_t$	Emission reduction costs
$Y_t$	Final output	$D_t$	Private emission reduction	$q_t$	Fossil fuel input efficiency
$N_t^Y$	Labor inputs (final output)	$M_t$	CO2 emissions	$B_t$	Government bond
$K_t^Y$	Capital inputs (final output)	$S_t$	CO2 stocks	$G_t$	Public expenditure
$P_t$	Overall price level	$P_t^{CO2}$	CO2 price	$R_t^B$	Government bond price
$f_t^{\mathit{EN}}$	Energy efficiency	$I_t$	Investment	$K_t$	Total capital
$S_t^c$	Subjective discount factor	$S_t^I$	Investment adjustment cost factor	$N_t$	Total labor
${\tau }_t^{\mathit{EN}}$	Fossil fuel tax rate	${\tau }_t^N$	Labor tax rate	${\tau }_t^K$	Capital tax rate

Author contribution

X. Guo, data curation, methodology, writing-review and editing.

B. Xiao, conceptualization, methodology, writing-original draft.

Funding

The National Natural Science Foundation of China (Grant No. 72204041); Humanities and Social Sciences Youth Foundation of Ministry of Education of China (Grant No. 22YJC790035); Humanities and Social Sciences Youth Foundation of Ministry of Education of China (Grant No. 22YJC790143).

Data availability

Not applicable.

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.